There ARE companies that encourage modding, although i know of precious few.
Valve (you may have heard of them), which had mods that practically outshone the original games in their popularity.
Zenimax/Bethesda, and their incredibly popular games.
Defunct:
Bioware, before EA ate them. Neverwinter Nights and Dragon Age: Origins both had very nice toolsets. NWN's enduring appeal with its DM client is legendary. (I realize DA:O was released after EA got ahold of it, but I believe most of the work was done by then.) Don't expect any sort of community support from an EA-run franchise; the only thing EA wants to hear players doing is typing in credit card numbers.
Iron Lore Entertainment (Titan Quest) included tools, and there was a decently healthy modding community around TQ. Notably, the publisher of the game was THQ, and here's
a little snippet of how they tried to ruin everything even then. This studio closed in 2008.
38 Studios / Big Huge Games, before The Collapse,
may have been planning to support modding. I've seen a quote of a post on the now-dead forum that reads, "Our ultimate goal will be to release our full tool set to our players to allow them to mod our games, any game, as much as they'd like.". That will of course never happen now, if it ever was intended.